A2.N.RN.A Extend the properties of exponents to rational exponents.
A2.N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
A2.N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
A2.N.Q.A Reason quantitatively and use units to solve problems.
A2.N.Q.A.1 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling.
A2.A.REI Reasoning with Equations and Inequalities
A2.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
A2.A.REI.A.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A2.A.REI.B Solve equations and inequalities in one variable.
A2.A.REI.B.3 Solve quadratic equations and inequalities in one variable.
A2.A.REI.B.3.a Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
A2.A.REI.D Represent and solve equations graphically.
A2.A.REI.D.6 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the approximate solutions using technology.
A2.F.IF.A Interpret functions that arise in applications in terms of the context.
A2.F.IF.A.1 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
A2.F.BF.B Build new functions from existing functions.
A2.F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
A2.F.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
A2.S.CP Conditional Probability and the Rules of Probability
A2.S.CP.A Understand independence and conditional probability and use them to interpret data.
A2.S.CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
A2.S.CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
A2.S.CP.A.3 Know and understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.